Heavy-Quark Thermalization

and Resonances in the QGP

Ralf Rapp Cyclotron Institute + Physics Department

Texas A&M University College Station, USA

With: H. van Hees (Texas A&M), V. Greco (Texas A&M, Catania)

Quark Matter 2005 Conference Budapest (Hungary), 06.08.05

1.) Introduction: Single-e± Spectra pre-QM05

Coalescence assuming v2(c) = v2(q) and/or jet quenching?

• dynamical origin of strong re-interactions• consistency v2 ↔ RAA

• open-bottom “contamination” • induced radiation vs. elastic scattering• …

Challenges:

pT [GeV/c]

RA

A

Djordjevic etal. ‘04

Armesto etal.‘05

jet-quench[Djordjevic etal ’04]

2.) Baseline Spectra in p-p, d-Au Charm vs. Bottom

3.) Heavy-Quark Elastic Scattering in QGP pQCD vs. Resonances Brownian Motion and Thermal Relaxation

4.) Heavy-Quark and Electron Spectra at RHIC Langevin Simulation, Hadronization RAA and v2

5.) Heavy Quarkonia Charmonium pT-Spectra

6.) Conclusions

Outline

2.) Heavy-Flavor Baseline Spectra at RHIC Single-Electron Decays D-Mesons

• bottom crossing at 5GeV !? (pQCD: ~4GeV [Cacciari etal ’05])• strategy: fix charm with D-mesons, adjust bottom in e±-spectra

TEtpp peetpf /2/)]([ 220

2

1),(

)1()( 22 teD

t

2

2

p

fD

p)pf(

tf

• Brownian Motion:

kpkwkdp ),(323 ),(

2

1 kpkwkdD

scatt. rate

diff. const.

3.) Elastic Heavy-Quark Scattering in the QGP

• e.g. T=400MeV, s=0.4 = 0.1 fm-1 ↔ therm~10fm/c slow!

3.1 Perturbative QCDg

c

q

c

• dominated by t-channel gluon-ex in gc→gc: gT~,~dtd

DD

s

2

2

Fokker Planck Eq.

[Svetitsky ’88,Mustafa etal ’98, Molnar etal ’04Zhang etal. ’04,Teaney+Moore‘04]

3.2 Open-Charm Resonances in QGP

h.c.2

v1 c)(

qG DDDcq L

• effective model with pseudo/scalar + axial/vector “D-mesons”

551 ,,,

“Light”-Quark Resonances

1.4Tc

[Asakawa+ Hatsuda ’03]

• parameters: mD(0)=2GeV , GD ,

mc=1.5GeV, mq=0 • number of D-states: 4 per u and d, 2 for s• cross section isotropic • more microscopic → [M.Mannarelli’s talk]

[van Hees+ RR ’04]

c

“D”

c

_q

_q

3.3 Heavy-Quark Thermalization Times in QGP

• substantially smaller for resonances

Charm: pQCD vs. Resonances

pQCD

“D”

• crelax ≥ (T>0.25GeV) ≈ 1fm/c

• bottom does not thermalize (10%)

Charm vs. Bottom

→ stochastic implementation of heavy quarks in expanding fireball with realistic time evolution of bulk v0 , v2

4.) Heavy-Quark and Electron Spectra at RHIC 4.1 Relativistic Langevin Simulations

[van Hees,Greco+RR ’05]

Nuclear Suppression Factor

• pQCD elastic scatt. moderate • resonance effects substantial

• characteristic “leveling-off”• factor ~4 from resonances

Elliptic Flow

frag2

2333

)p(f)p(f|)q(|qd)(

pdg

pd

dNE ccqqDD

D

4.2 Single-Electron v2 and RAA at RHIC fq from, K

coalescence+ fragment.

[van Hees, Greco +RR ’05]

• coalescence increases both RAA and v2 , resonances essential• bottom contribution reduces effects• induced gluon radiation?

Elliptic Flow Nuclear Suppression FactorMinimun-BiasAu-Au 200GeV

Minimun-BiasAu-Au 200GeV

5.) J/ pt-Spectra in Au-Au at RHIC

• total yields different by factor 3

• large sensitivity to radial flow (t,max=0.5-0.65)

[Thews+Mangano ’05]

[Greco,Ko+RR ’04]

Quark Coalescence at Tc

6.) Summary

• “D”-meson resonances in QGP (lQCD spectral fcts., potentials) c(b)-quark thermalization ~4(12)fm/c (elastic scattering), (factor ~3 faster than pQCD)

• Langevin simulation for RHIC + coalescence/fragmentation: - electrons: v2 ≤ 11% , RAA ≥ 0.45 (MinBias), “compromised” by bottom - predictions similar to new PHENIX data

• sQGP elastic scattering (resonances) prevalent over radiation at low / medium pt !?

• (more) uncertainties: hadronic phase (lifetime), smaller mc (?), bottom contribution, softer fragmentation

• impact on quarkonia, dileptons (intermediate mass)

3.) Resonances in QGP: Microscopic Description Lattice Q-Q Free Energy

TSUF QQQQ

QQQ mU 2

[BielefeldGroup ’04]

Applications

• → Schröd.-Eq. → bound states (sQGP)!

• scattering states? imaginary parts? → Lippmann-Schwinger Equation

QQU[Shuryak,Zahed, Brown ’04]

Selfconsistency Problem[Mannarelli+RR ’05]

q-q T-Matrix -

Quark-Selfenergy

3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05]

• assume mq(gluon)=0.1GeV

• transition from bound (1.2Tc) to resonance states! • quark-width ≈0.3GeV≈(2/3fm)-1 (≈ mass ↔ liquid!?) • colored states, equat. of state?

q-q T-Matrices -

Quark Self-

Energy

T=1.2Tc

T=1.5Tc

T=1.75Tc

T=1.5Tc

Individual Charm- and Bottom-Electron RAA and v2

2.4.2 Langevin-Simul. at RHIC: Heavy-Quark v2

Resonances vs. pQCD Charm-pQCD (s, D=1.5T)

[van Hees,Greco+RR ’05]

• characteristic “leveling-off”• factor ~4 from resonances • more sensitive to res.-coupling

• hydro with Tc=165, ≈ 9fm/c

• s and Debye mass independent[Moore and Teaney ’04]

2.4.1 Langevin-Simul. at RHIC: Heavy-Quark RAA

[van Hees,Greco+RR ’05]

Resonances vs. pQCD Charm-pQCD (s, D=1.5T)s , g

1 , 3.5

0.5 , 2.5

0.25,1.8

[Moore and Teaney ’04]

• hydro with Tc=165MeV, ≈ 9fm/c

• s and Debye mass independent

• expanding fireball ≈ hydro • pQCD elastic scatt. moderate • resonance effects substantial

c-Quark Drag and Diffusion Coefficients in QGP

• substantially smaller for resonances

Thermalization Times [van Hees+RR ’04]

pQCD

“D”

Coordinate Space Diffusion

• ‹x2› - ‹x›2 = Dx t ≈ (5 fm)2

~ fireball size at Tc

• QGP-suppression prevalent• no “jump” in theory

• QGP-regeneration dominant• sensitive to: mc

* , (Ncc )2 ↔ rapidity, √s, A

4.4 Charmonium in A-A

SPS RHIC

[Grandchamp etal. ’03]

Pb(158AGeV)-Pb

[Grandchamp +RR ’03]

J/ Excitation Function

same net suppression at SPS + RHIC!

3.4.3 Scrutinizing Charmonium Regeneration II: J/ Elliptic Flow

Suppression only Thermal Coalescence at Tc

[Wang+Yuan ’02]

[Greco etal ’04]

MB Au-Au

• factor ~5 different! • transition in pt!?